Child seats for children are well known children's appliances and are already commercially available. In order to facilitate storing, most of the child seats for children are usually designed in a collapsible form. For instance, U.S. Pat. No. 6,854,800 has disclosed a collapsible child seat. As illustrated in FIG. 4 of the U.S. Pat. No. 6,854,800 patent, the child seat can be collapsed from a extended state (as illustrated in FIG. 1) to a collapsed stated (as illustrated in FIG. 2) by operating the operation handle 26 to pull transmission cables 27 to disengage the pins 29 from the engagement holes 31. Although the collapsing device of the U.S. Pat. No. 6,854,800 patent, i.e., including the handle 26, the cables 27, the pins 29, and the engagement holes 31 etc., can achieve the function of collapsing the child seat, however, it takes two hands to properly operate/collapse the child seat and this causes inconvenience in use. Therefore, there exists a need for a collapsing device of a child seat which allows the user to effectively perform the collapsing operation of the child seat with one hand in a one-step operation.